标题： 一种用于三维不可压缩流动的高阶半显式不连续伽辽金求解器及其在湍流通道流动直接数值模拟和大涡模拟中的应用 显示英文标题

标题： A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow

摘要： 我们提出了一种高效的不连续伽辽金方案，用于模拟不可压缩纳维-斯托克斯方程，包括层流和湍流。 我们考虑一种半显式高阶速度校正方法进行时间积分，以及节点等阶离散化处理速度和压力。 非线性对流项被显式处理，而压力泊松方程和粘性项则求解一个线性系统。 我们求解器的关键特性是一个一致的惩罚项，用于减少局部发散误差，以克服最近在空间欠分辨的高雷诺数流动以及小时间步长下报告的不稳定性。 该惩罚方法类似于在连续有限元中广泛使用的梯度-散度稳定化方法。 我们进一步回顾并比较了我们的方法与文献中最近提出的几种其他技术，以稳定这种流动配置的方法。 该求解器通过无矩阵线性求解器专门设计用于大规模计算，包括高效的预条件策略和张量积单元，这使得我们能够将该代码扩展到344亿自由度和147,456个CPU核心。 我们验证了我们的代码，并通过涡旋问题和圆柱体后的流动展示了层流中的最优收敛率，并展示了我们的求解器在直接数值模拟以及湍流通道流动的隐式大涡模拟中的适用性，其雷诺数为$Re_{\tau}=180$以及$590$。 显示英文摘要

摘要： We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration as well as nodal equal-order discretizations for velocity and pressure. The non-linear convective term is treated explicitly while a linear system is solved for the pressure Poisson equation and the viscous term. The key feature of our solver is a consistent penalty term reducing the local divergence error in order to overcome recently reported instabilities in spatially under-resolved high-Reynolds-number flows as well as small time steps. This penalty method is similar to the grad-div stabilization widely used in continuous finite elements. We further review and compare our method to several other techniques recently proposed in literature to stabilize the method for such flow configurations. The solver is specifically designed for large-scale computations through matrix-free linear solvers including efficient preconditioning strategies and tensor-product elements, which have allowed us to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores. We validate our code and demonstrate optimal convergence rates with laminar flows present in a vortex problem and flow past a cylinder and show applicability of our solver to direct numerical simulation as well as implicit large-eddy simulation of turbulent channel flow at $Re_{\tau}=180$ as well as $590$.